Effect of internal heat generation on the onset of Brinkman–Benard convection in a ferrofluid saturated porous layer

Abstract

The effect of internal heat generation on the criterion for the onset of convection in a horizontal ferrofluid saturated porous layer in the presence of a uniform magnetic field is studied using the Brinkman–Lapwood extended Darcy flow model with fluid viscosity different from effective viscosity. The lower boundary is taken to be rigid – isothermal and the upper surface is free and subject to the general thermal condition. The resulting eigenvalue problem is solved numerically using the Galerkin method with the Rayleigh number as the eigenvalue. The stability of the system is found to be dependent on the dimensionless internal heat source strength N s , Darcy number Da, viscosity ratio Λ , Biot number Bi, magnetic Rayleigh number, R m and the nonlinearity of fluid magnetization parameter M 3. The effect of increase in the value of R m , N s and M 3 is to hasten, while increase in the value of Bi, Λ and Da −1 is to delay the onset of thermomagnetic convection in a ferrofluid saturated porous layer. Further, increase in the value of Bi, Da −1 and N s as well as decrease in Λ , R m and M 3 is to diminish the dimension of convection cells.